where \(x_t \in \mathbb {R}^{n_x}\)  and \(u_t \in \mathbb {R}^{n_u}\)  are the vectors of states and inputs, respectively, and \(\phi :\mathbb {R}^{n_x} \times \mathbb {R}^{n_u} \mapsto \mathbb {R}^{n_x}\)  is some smooth state transition function.
In such systems, the optimal control problem that must be solved in the context of model predictive control [1]} can be brought into the form of (REF ) by introducing additional variables \(\tilde{x}_{t} \in \mathbb {R}^{n_x}\)  and additional constraints:
\(x_{t+1} = \tilde{x}_{t}, \;\; \tilde{x}_{t} = \phi (x_t, u_t),\) 
